Abstract: The invention relates to a process and the associated device for the fine crushing of solid mineral and non-mineral substances, preferably cement raw materials and cement clinker, by single or repeated compressive-load application using medium to high pressures with subsequent disagglomeration of the produced ground material in the same device. The object of the invention is to create a crushing device which, under defined conditions of control of, and load application by, the material to be ground, combined in a single device, carries out several process steps in succession, continuously feeds the material to be ground, as a defined material layer, to the grinding gap formed from pressure roller and level load-application path and, through the free choice of grinding path speed and grinding pressure, has a favorable throughput behavior with a high energy utilization and low outlay on plant.